Making a substantiated choice of the most efficient statistical test of several ones being at the disposal of the statistician is regarded as one of the basic problems of statistics. According to the classical Neyman--Pearson theory the most powerful uniform tests are considered the best. However it is widely known that they exist merely in a narrow class of statistical models which do not fully cover the diversity of problems arising in theory and practice. One can still say that within the framework of parametric statistics this problem is not at all crucial. The point is that quite formal methods of constructing tests have been developed, e.g., Bayes or likelihood ratio. They possess a number of remarkable properties and usually turn out to be asymptotically optimal in a sense of one or another definition of this concept. Therefore the problem of comparing nonparametric tests on the basis of some quantitative characteristic that will make it possible to realize ordering these